# Day of the Week Calculation - Thoughts

About six years ago, I learned the Doomsday algorithm for computing dates, which relies on the fact that the last day of February, 4/4, 6/6, 8/8, 10/10, and 12/12 all fall on the same day of the week every year. Which day of the week this is is called the Doomsday for that year. Unfortunately, I do not have such a technique for easily recalling these Doomsdays, so I rely on a bit of calculation. My current strategy is as follows:

1. Use your left hand (or right hand if you’re like me and left-handed) and assign the fingers from Monday to Friday. Saturday and Sunday will be the gaps on either side - a “missing finger” if you will.

2. For 1900, start on Wednesday. For 2000, start on Tuesday.

3. Add 28 repeatedly - 28, 56, 84 (e.g. 1928, 1956…). You don’t move your finger during this calculation. Stop before you overflow (go past the year you want).

4. Add 4 repeatedly, moving back two fingers every time you do so. Again, stop before you overflow.

5. Add 1 for each year after that, moving forward one finger each time until you reach your desired year. The result will be the Doomsday.

For example, 1983. I would start on Wednesday for 1900, 1928, 1956, and move back twelve fingers until 1980, and move forward three for 1983. The result of the calculation is a Monday Doomsday, but it takes me about 5 seconds to compute this rapidly. From there, I have to calculate the month and day, which in a worst-case scenario is another 5 seconds. The finger I end up on is the result for that day.

Also, I don’t want to have to rely on a physical method for determining the day of the week. I wish I could do it mentally, and faster. (For calculating a calendar day this year for example - I still have to calculate the Doomsday for the year! 2000, 2004, 2008, 2012, 2016, 17, 18, 19… it’s Thursday. October 10 is Thursday, so calculate from there.)

I wonder if there’s an easier method. What am I doing that’s inefficient? Could I reduce the problem to a list of codes or a memory palace, placing all of the Tuesdays together or trying to link 19 (a roll of tape in my Major system) to 4 (Thursday - FOURSday, I start from 1 on Monday)?

Hmmm…

2 Likes

There is… century code + year code + month code + day, divide by seven, and take the remainder. In case the date is Jan/Feb in a leap year subtract one. That’s all… easily under 5 seconds for the entire date.

Have a look here for how to set up the memory palaces for the year codes:

2 Likes

I was thinking more about the month and year codes.

I’ve found that there are two competing standards - the Doomsday algorithm (which is what I naturally use, 2000 = Tuesday (2), 2001 = Wednesday (3), etc.) and the traditional year code, which is 2 off for the 2000s. (2000 = 0, 2001 = 1 , etc.) I’ll use the traditional year code to ease memorization. My mnemonics are below, so feel free to come up with something else that’s more vivid for you.

Day - 1-31 unchanged

Months
January - 6 - A New Year’s countdown, but they get stuck on SIX, SIX, SIX, SIX, SIX…
February - 2 - February is the second month.
March - 2 - MARCH TWO the beat.
April - 5 - APRIL FOOLS both have 5 letters.
May - 0 - You MAY NOT have anything.
June - 3 - JUNE SUN - Sun has 3 letters.
July - 5 - FIVERworks.
August - 1 - AUGUST is ONE hot month.
September - 4 - SEPTEMBER is FOR (four) the new students.
October - 6 - SIX-or-treat!
November - 2 - NOOOOO!-vember, can we get TWO more months? Pleeease?
December - 4 - I long FOUR my seasonal depression to end this month…

2000 - 0 - Easy
2001 - 1 - Easy…
2002 - 2 - Yawn…
2003 - 3 - Snore…
2004 - 5 - Huh, what? Uh, the SOUR patch kids some in FIVE colors.
2005 - 6 - The CELL has SIX nuclei (that’s impossible biologically, so that works for me)
2006 - 0 - The lightSWITCH is turned OFF (zero).
2007 - 1 - I need a SOCK. I only have ONE.
2008 - 3 - A SOFA with room for THREE people on it.
2009 - 4 - Fresh SOAP FOUR my body.
2010 - 5 - DICE, but they’re all FIVE-sided dice. (What would that even look like? Hmmm…)
2011 - 6 - SIX TOADS singing a horrible song.
2012 - 1 - A huge DINO with only ONE tooth.
2013 - 2 - My best friend on the TEAM is player number TWO.
2014 - 3 - My TIRE went flat, so I only have THREE.
2015 - 4 - I have only FOUR TOWELS, one for each season. (Weird memory from when I was young.)
2016 - 6 - I’d like SIX DISHES of yummy food, please.
2017 - 0 - A DECK of cards vanishes into NOTHING.
2018 - 1 - Noah sent ONE DOVE out from the Ark.
2019 - 2 - I wrap TAPE around my hockey stick only TWICE.
2020 - 4 - NASA discovers FOUR new planets in the solar system.
2021 - 5 - NOTE to self: I’m still ALIVE (a FIVE, minor pun.)
2022 - 6 - A NEON sign glows in all SIX colors of the rainbow.
2023 - 0 - I FORGOT my NAME! (forgot = zero.)
2024 - 2 - It’s an HONOR to give you TWO Ph.D’s!
2025 - 3 - THREE NAILS hold up the shelf.
2026 - 4 - The NACHOS are FOUR my friends.
2027 - 5 - NUKE the FIVE major UN countries (US, UK, France, Russia, China).
2028 - 0 - A NOVA VOIDS everything.
2029 - 1 - I have ONE broken pen NIB.
2030 - 2 - This has a MASS of TWO kilograms.
2031 - 3 - My neighbor has a strange welcome MAT. It has THREE corners.
2032 - 5 - Earth has FIVE MOONS?!
2033 - 6 - This MUMMY was wrapped in bandages SIX times.
2034 - 0 - Thanos has a HAMMER that VOIDS everything.
2035 - 1 - You have ONE piece of MAIL.
2036 - 3 - THREE MATCHES in a triangle.
2037 - 4 - I use my MIC FOUR singing the FOUR SONG. (1-2-3-4…)
2038 - 5 - I went to a MOVIE at FIVE o’clock.
2039 - 6 - The MAP shows all SIX major inhabited continents. (Sorry, Antarctica…)
2040 - 1 - I ran a RACE and got FIRST PLACE.
2041 - 2 - Robert Frost - TWO ROADS poem.
2042 - 3 - It’s scheduled to RAIN at THREE o’clock.
2043 - 4 - ARMY has FOUR letters.
2044 - 6 - An ORRERY usually shows the first SIX planets.
2045 - 0 - A mean ROYAL ordered the DEATH OF EVERYONE (= ZERO people left).
2046 - 1 - RUSSIA is number ONE in area.
2047 - 2 - I split a ROCK into TWO.
2048 - 4 - RAVE has FOUR letters.
2049 - 5 - I used my ROPE to climb a distance of FIVE meters.
2050 - 6 - I had to tie my LACES SIX times today.
2051 - 0 - The LID fits NO jar.
2052 - 2 - TWO LIONS attack me at the same time!
2053 - 3 - LIME juice in the eyes of a THREE-EYED creature!
2054 - 4 - I give my support FOUR the OILER.
2055 - 5 - FIVE, FIVE, must be FIVE!
2056 - 0 - The LATCH makes ZERO criminals enter my house.
2057 - 1 - The view of ONE giant LAKE.
2058 - 2 - TWO volcanoes erupt LAVA.
2059 - 3 - THREE scientists that I know are working in the LAB.
2060 - 5 - CHEESE with FIVE holes. (stick your hand through the cheese so each finger goes through one of the holes.)
2061 - 6 - A JET that only carries SIX people.
2062 - 0 - A CHAIN in a loop, creating the number ZERO and also being useless to chain anything together.
2063 - 1 - ONE rare GEM!
2064 - 3 - THREE old smelly JARS of something horrible.
2065 - 4 - A JELLO square has FOUR corners.
2066 - 5 - JUDGE has FIVE letters.
2067 - 6 - A football JOCK wearing the number SIX.
2068 - 1 - One angry CHIEF.
2069 - 2 - A massive JEEP painted in TWO bright neon colors.
2070 - 3 - A suitCASE holding THREE classified documents.
2071 - 4 - The CAT has FOUR legs.
2072 - 6 - A stack of SIX CANS.
2073 - 0 - A new and exciting board GAME where NO ONE plays.
2074 - 1 - I bought ONE CAR for myself.
2075 - 2 - A COILed spring that bounces TWO meters.
2076 - 4 - I have CASH from FOUR interesting countries.
2077 - 5 - A CAKE to celebrate someone’s FIFTH birthday.
2078 - 6 - A CAVE where you can travel in SIX directions.
2079 - 0 - I lend out my favorite CAP to NO ONE.
2080 - 2 - The VASE shattered into TWO pieces.
2081 - 3 - THREE hockey players got involved in a FIGHT.
2082 - 4 - VINES cover all FOUR sides of my house.
2083 - 5 - FOAM is used by FIVE people for their baths.
2084 - 0 - FIRE DESTROYS all.
2085 - 1 - ONE piece of FOIL.
2086 - 2 - I caught TWO FISH today.
2087 - 3 - FIG has THREE letters.
2088 - 5 - FIVE trespassers entered the FIEF (a medieval plot of land).
2089 - 6 - SIX people are VAPE-ing around me, eugh.
2090 - 0 - The wheels on the BUS are shaped like ZERO.
2091 - 1 - I only took ONE BOOT with me on my hiking trip.
2092 - 3 - The arm has THREE BONES.
2093 - 4 - FOUR laser BEAMS are directed at Earth from space.
2094 - 5 - FIVE BEARS are out to eat us!
2095 - 6 - I’m playing a sport with SIX BALLS.
2096 - 1 - ONE BADGE for a trusted officer.
2097 - 2 - TWO BOOKS are in my collection, both reference works.
2098 - 3 - He’s so BUFF that he can list THREE hundred kilograms.
2099 - 4 - Hit on the head with a PIPE FOUR times.

2 Likes

It doesn’t make sense to add 2 every time you want to get the year code. Read my linked post and put the years that come out 0 (i.e., 00, 06, 17, 23, etc.) and put them in your Tuesday palace instead of your Sunday palace, as I describe it. Then you simply get 2 when you do the \color{blue}Memory Palace Reverse Lookup\ \#MPRL and just repeat offsetting all the years by 2 when you place them in the 7 palaces.

Correct, you can do mod 7 if you don’t like working with large numbers at the end. If the days are 7, 14, 21, or 28; I don’t add the code for say July to get 12, 19, 26, and 33; but just drop the day and work with only 5. Similarly, I drop day + month code if together they come out 0.

But that is optional. It’s not really a calculation in my head… it’s more like playing Tetris and 3 lines of 7s disappear when you get {\color{blue}Jun\ 18} \to 3+18=21. That 21 is just gone.

If that works for you… I’ve pointed out in the linked post that ApriL and JuLI, the only two months with an L, are the major code for L = 5. June ends with an E which is 3 written backwards. The only month left starting with a J (January) has the major value for J = 6.

Feb is special with only 28 days and keeps it’s value of 2. November is the second from the end, so you could argue symmetry. Also adding together 1+1 for the 11th months makes 2. March is also 2 because February wasn’t long enough. These are more illogical arguments as mnemonics.

The last four months all end in R which is major code 4; however, November is already 2, so October needs to be 6 for an average of 4. It also raises the philosophical question if you’d rather have an octopus with 6 legs and 2 arms or rather 6 arms and 2 legs, if you were a restaurant owner.

Leaves the condiments: May0nnaise and A1 sauce or A as the 1st letter of the alphabet. I’m not saying that you should use mine, but rethink or add logic to yours. You can’t be counting the letters in “April” or “Fools” and “March to the beat” I’ve seen on the internet before… you should always use your own mnemonics that make sense to you.

I assume here is where you lose most of your time. Read the post I’ve linked above. You need a set of 7 memory palaces and then pick the palace the year is in. It’s all explained in that post, so I’m NOT going to write it all here again.

2058 - 2 - plus 0 for the century = 2.
1958 - 2 - plus 1 for the century = 3.
1858 - 2 - plus 3 for the century = 5.
1758 - 2 - plus 5 for the century = 0.
1658 - 2 - plus 0 for the century.

Just adding the centuries for completeness, unless you only want to do years between 2000-2099… in which case ignore this last bit.

Thanks. I might use seven memory palaces. We’ll see how well it works (assuming I don’t forget about this).

Dragons and dungeons and other rpg games use five sided dice.

Lol… fair enough.

I assume you review your 2-digit system from time-to-time, so this way you can review it in pseudo random order that the mini-palaces give you and kill two birds with one stone… review your 00-99 system as well as the year codes.

The random order is nice, so you don’t get stuck with only knowing 47 in your system if it follows the image for 46. An issue that happens sometimes when the review order is always the same.

I review my 2-digit system from time to time actually. Random order is nice - I like to test myself on 10-digit numbers.